New explicitly diagonalizable Hankel matrices related to the Stieltjes-Carlitz polynomials
Abstract
Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter $k\in(0,1)$ are presented. The Hankel matrices are regarded as matrix operators on the Hilbert space $\ell^{2}(\mathbb{N}_{0})$ and the solution of the spectral problem is based on an application of the commutator method. Each of the Hankel matrices commutes with a Jacobi matrix which is related to a particular family of the Stieltjes-Carlitz polynomials. More examples of explicitly diagonalizable structured matrix operators are obtained when taking into account also weighted Hankel matrices.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.08218
- arXiv:
- arXiv:1911.08218
- Bibcode:
- 2019arXiv191108218S
- Keywords:
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- Mathematics - Spectral Theory;
- Mathematics - Classical Analysis and ODEs